Improvement of Monte Carlo estimates with covariance-optimized finite-size scaling at fixed phenomenological coupling
|
|
- Clare Sims
- 6 years ago
- Views:
Transcription
1 Improvement of Monte Carlo estimates with covariance-optimized finite-size scaling at fixed phenomenological coupling Francesco Parisen Toldin Max Planck Institute for Physics of Complex Systems Dresden 25 November 2011 F. Parisen Toldin (MPI PKS) FSS at fixed phenomenological coupling 25 November / 13
2 Monte Carlo methods Powerful and flexible method to study critical phenomena General feature: accuracy 1 computational time In order to improve the accuracy: improved estimators Use of covariance analysis: - add control variates, whose expectation value vanish 1 - compute the optimal weighted average of different estimates of a critical exponent 2 Our method: - Optimization of a Finite-Size Scaling method - It allows for a significant reduction of the error bars - It does not require additional computational time 1 L. A. Fernández, V. Martín-Mayor, Phys. Rev. E 79, (2009) 2 M. Weigel, W. Janke, Phys. Rev. Lett. 102, (2009); Phys. Rev. E 81, (2010) F. Parisen Toldin (MPI PKS) FSS at fixed phenomenological coupling 25 November / 13
3 Finite-Size Scaling A system in a finite volume of linear size L Finite-Size Scaling (FSS) works in region of parameters where ξ L FSS behavior of long-ranged quantities O = L x f (tl 1/ν ), t T T c T c E.g. Susceptibility χ L 2 η f (tl 1/ν ) Renormalization-Group invariant quantities R R = F(tL 1/ν ) E.g. R = ξ/l, Binder ratios, etc... Also called phenomenological couplings F. Parisen Toldin (MPI PKS) FSS at fixed phenomenological coupling 25 November / 13
4 Finite-Size Scaling at fixed phenomenological coupling We fix a phenomenological coupling R to a constant R f R(β,L) = R f β f (L) such that R(β f (L), L) = R f From FSS relation R = F(tL 1/ν ), t = (T T c )/T c = β c /β 1: β f (L) β c L 1/ν, β f (L) β c L 1/ν ω, generic R f R f = R = F(0) All the other observables O(β,L) are calculated at β = β f (L) χ(β f (L), L) L 2 η, R β (β f (L), L) L 1/ν susceptibility M. Hasenbusch, J. Phys. A 32, 4851 (1999) F. Parisen Toldin (MPI PKS) FSS at fixed phenomenological coupling 25 November / 13
5 Finite-Size Scaling at fixed phenomenological coupling It does not require a precise knowledge of β c Reduced error bars by fixing ξ/l: - Fully frustrated XY model 1 - Randomly Dilute Ising Universality class 2 - Ising model in d = 3, 4, 5 3 Similarities with the Phenomenological Renormalization method: - Two system sizes are enforced to share a common value of ξ/l - Reported reduction of error bars 4 1 M. Hasenbusch, A. Pelissetto, E. Vicari, JSTAT P12002 (2005) 2 M. Hasenbusch, F. Parisen Toldin, A. Pelissetto, E. Vicari, JSTAT P02016 (2007) 3 U. Wolff, Phys. Rev. D 79, (2009) 4 H. G. Ballesteros, L. A. Fernández, V. Martín-Mayor, A. Muñoz-Sudupe, Nucl. Phys. B 483, 707 (1997) F. Parisen Toldin (MPI PKS) FSS at fixed phenomenological coupling 25 November / 13
6 Finite-Size Scaling at fixed phenomenological coupling Why there is a reduction of the error bars? Notation: Simulations at β = β run An observable O is calculated from a statistical estimator Ô Ô = O + δo, O = E[Ô] We choose to fix a phenomenological coupling R sampled using the estimator R We fix R(β = β f (L), L) = R f and calculate O f (L) O(β = β f, L) F. Parisen Toldin (MPI PKS) FSS at fixed phenomenological coupling 25 November / 13
7 Finite-Size Scaling at fixed phenomenological coupling For β close to β run R(β) R + R (β β run ), R = R(βrun ), R = R/ β. Solving R = R f βf = βrun R R f R we trade the fluctuations of R for the fluctuations of β f For a generic observable O calculated at β f Ô f Ô + Ô (β β run ) = Ô Ô R R f R. The variance of Ôf is, to the lowest order in the fluctuations ( ) O 2 VAR[Ôf ] = VAR[Ô] + R VAR[ R] 2 O COV[Ô, R] R F. Parisen Toldin (MPI PKS) FSS at fixed phenomenological coupling 25 November / 13
8 Optimization of Finite-Size Scaling Can we optimize the Finite-Size Scaling? Consider N phenomenological couplings R 1,...,R N We define the RG-invariant quantity R({λ i }) i λ ir i We consider FSS at fixed phenomenological coupling R({λ i }) Problem: given an observable O, what are the coefficients {λ i } that minimize the value of O f? Minimize: VAR[Ôf ] = VAR[Ô] + ( O R ) 2 VAR[ R] 2 O COV[Ô, R] R Solution: λ i = R T M 1 N O ( R T M 1 R M 1 R ) ) (M + 1 N, i i with M ij COV[ R i, R j ], N i COV[Ô, R i ], R i R i. F. Parisen Toldin (MPI PKS) FSS at fixed phenomenological coupling 25 November / 13
9 Optimization of Finite-Size Scaling Can we optimize the Finite-Size Scaling? Consider N phenomenological couplings R 1,...,R N We define the RG-invariant quantity R({λ i }) i λ ir i We consider FSS at fixed phenomenological coupling R({λ i }) Problem: given an observable O, what are the coefficients {λ i } that minimize the value of O f? Minimize: VAR[Ôf ] = VAR[Ô] + ( O R ) 2 VAR[ R] 2 O COV[Ô, R] R Solution: λ i = R T M 1 N O ( R T M 1 R M 1 R ) ) (M + 1 N, i i with M ij COV[ R i, R j ], N i COV[Ô, R i ], R i R i. F. Parisen Toldin (MPI PKS) FSS at fixed phenomenological coupling 25 November / 13
10 Optimization of Finite-Size Scaling Can we optimize the Finite-Size Scaling? Consider N phenomenological couplings R 1,...,R N We define the RG-invariant quantity R({λ i }) i λ ir i We consider FSS at fixed phenomenological coupling R({λ i }) Problem: given an observable O, what are the coefficients {λ i } that minimize the value of O f? Minimize: VAR[Ôf ] = VAR[Ô] + ( O R ) 2 VAR[ R] 2 O COV[Ô, R] R Solution: λ i = R T M 1 N O ( R T M 1 R M 1 R ) ) (M + 1 N, i i with M ij COV[ R i, R j ], N i COV[Ô, R i ], R i R i. F. Parisen Toldin (MPI PKS) FSS at fixed phenomenological coupling 25 November / 13
11 Some observations Finite-Size Scaling at fixed R({λ i }) i λ ir i, with λ i = R T M 1 N O ( R T M 1 R M 1 R ) ) (M + 1 N, i i M ij COV[ R i, R j ], N i COV[Ô, R i ]. M and N are related to the transition matrix of the Markov chain they depend on the model and on the dynamics {λ i } can be optimized separately for every observable O FSS limit is correctly defined when {λ i } are the same for all sizes. The optimal {λ i } depend on the lattice size. Possible strategy: choose the optimal {λ i } obtained from the largest available lattice. F. Parisen Toldin (MPI PKS) FSS at fixed phenomenological coupling 25 November / 13
12 Test: Ising model in d = 2, 3 H = J ij Four RG-invariant quantities: σ i σ j, σ i = ±1. U 4 M4 M 2 2, U 6 M6 M 2 3 R ξ ξ/l, R Z Z a /Z 1 p, with M i σ i magnetization, ξ second-moment correlation length Z a partition function with antiperiodic b.c. on one direction, Z p partition function with fully periodic b.c. Observables χ i σ i σ j /V L 2 η 1 M.Hasenbusch, Physica A 197, 423 (1993) U 4 β, U 6 β, R ξ β L1/ν F. Parisen Toldin (MPI PKS) FSS at fixed phenomenological coupling 25 November / 13
13 Results d = 2 Gain in CPU time is given by ( ) standard error bar 2 error bar at fixed R CPU gain for Metropolis dynamics χ: gain 20; gain at fixed R ξ 4 U 4 / β, U 6 / β: gain 30 50; gain at fixed U 4, U R ξ / β: gain 2 3; gain at fixed U 4, U 6, R ξ, R Z 1 CPU gain for Wolff single-cluster dynamics χ: gain 6; gain at fixed R ξ 3 U 4 / β, U 6 / β: gain 6 9; gain at fixed U 4, U R ξ / β: gain 2 3; gain at fixed U 4, U 6, R ξ, R Z 1 Gain in computational time roughly independent on L = F. Parisen Toldin (MPI PKS) FSS at fixed phenomenological coupling 25 November / 13
14 Results d = 3 Gain in CPU time is given by ( ) standard error bar 2 error bar at fixed R CPU gain for Metropolis dynamics χ: gain 20 30; gain at fixed R ξ 9 U 4 / β, U 6 / β: gain 20 30; gain at fixed U 4, U 6 3 R ξ / β: gain 4 6; gain at fixed U 4, U 6, R ξ, R Z 1 CPU gain for Wolff single-cluster dynamics χ: gain 6 10; gain at fixed R ξ 5 U 4 / β, U 6 / β: gain 5 8; gain at fixed U 4, U R ξ / β: gain 3; gain at fixed U 4, U 6, R ξ, R Z 1 Gain in computational time roughly independent on L = F. Parisen Toldin (MPI PKS) FSS at fixed phenomenological coupling 25 November / 13
15 Outlook Substantial reduction of the error bars It does not require additional computational time Test on the Ising model - CPU gains are roughly independent on the lattice L - CPU gains are more pronounced for Metropolis update Other possible applications: - Improved models - Models with quenched disorder -... Ref: F. Parisen Toldin, Phys. Rev. E 84, (R) F. Parisen Toldin (MPI PKS) FSS at fixed phenomenological coupling 25 November / 13
arxiv:cond-mat/ v2 [cond-mat.dis-nn] 14 May 1998
1 arxiv:cond-mat/9805125v2 [cond-mat.dis-nn] 14 May 1998 Scaling corrections: site-percolation and Ising model in three dimensions H. G. Ballesteros a, L. A. Fernández a, V. Martín-Mayor a, A. Muñoz Sudupe
More informationShort-Time Critical Dynamics of the Three-Dimensional Systems with Long-Range Correlated Disorder
973 Progress of Theoretical Physics, Vol. 117, No. 6, June 2007 Short-Time Critical Dynamics of the Three-Dimensional Systems with Long-Range Correlated Disorder Vladimir V. Prudnikov, 1, ) Pavel V. Prudnikov,
More informationarxiv: v1 [cond-mat.stat-mech] 9 Feb 2012
Magnetic properties and critical behavior of disordered Fe 1 x Ru x alloys: a Monte Carlo approach I. J. L. Diaz 1, and N. S. Branco 2, arxiv:1202.2104v1 [cond-mat.stat-mech] 9 Feb 2012 1 Universidade
More informationarxiv: v1 [cond-mat.dis-nn] 7 Sep 2007
Short-time critical dynamics of the three-dimensional systems with long-range correlated disorder Vladimir V. Prudnikov 1,, Pavel V. Prudnikov 1, Bo Zheng 2, Sergei V. Dorofeev 1 and Vyacheslav Yu. Kolesnikov
More informationTheir Statistical Analvsis. With Web-Based Fortran Code. Berg
Markov Chain Monter rlo Simulations and Their Statistical Analvsis With Web-Based Fortran Code Bernd A. Berg Florida State Univeisitfi USA World Scientific NEW JERSEY + LONDON " SINGAPORE " BEIJING " SHANGHAI
More informationarxiv: v3 [cond-mat.dis-nn] 4 Jan 2018
The bimodal Ising spin glass in dimension two : the anomalous dimension η P. H. Lundow Department of Mathematics and Mathematical Statistics, Umeå University, SE-901 87, Sweden I. A. Campbell Laboratoire
More informationCURVE is the Institutional Repository for Coventry University
Critical aspects of three-dimensional anisotropic spin-glass models Papakonstantinou, T., Fytas, N., Malakis, A. and Lelidis, I. Author post-print (accepted) deposited in CURVE April 2016 Original citation
More informationIs there a de Almeida-Thouless line in finite-dimensional spin glasses? (and why you should care)
Is there a de Almeida-Thouless line in finite-dimensional spin glasses? (and why you should care) Peter Young Talk at MPIPKS, September 12, 2013 Available on the web at http://physics.ucsc.edu/~peter/talks/mpipks.pdf
More informationarxiv: v1 [cond-mat.stat-mech] 7 Dec 2016
EPJ manuscript No. (will be inserted by the editor) Scaling and universality in the phase diagram of the 2D Blume-Capel model arxiv:1612.02138v1 [cond-mat.stat-mech] 7 Dec 2016 J. Zierenberg 1,4, N. G.
More informationPhase Transitions in Spin Glasses
Phase Transitions in Spin Glasses Peter Young Talk available at http://physics.ucsc.edu/ peter/talks/sinica.pdf e-mail:peter@physics.ucsc.edu Supported by the Hierarchical Systems Research Foundation.
More informationarxiv: v1 [cond-mat.stat-mech] 2 Aug 2011
Anisotropic perturbations in three-dimensional O(N)-symmetric vector models Martin Hasenbusch Institut für Physik, Humboldt-Universität zu Berlin, Newtonstr. 15, 12489 Berlin, Germany Ettore Vicari Dipartimento
More informationarxiv:cond-mat/ v1 [cond-mat.stat-mech] 1 Jul 2006
Eliminated corrections to scaling around a renormalization-group fixed point: Transfer-matrix simulation of an extended d = 3 Ising arxiv:cond-mat/0607008v1 [cond-mat.stat-mech] 1 Jul 2006 model Yoshihiro
More informationMonte Carlo Study of Planar Rotator Model with Weak Dzyaloshinsky Moriya Interaction
Commun. Theor. Phys. (Beijing, China) 46 (2006) pp. 663 667 c International Academic Publishers Vol. 46, No. 4, October 15, 2006 Monte Carlo Study of Planar Rotator Model with Weak Dzyaloshinsky Moriya
More informationPhase transitions and finite-size scaling
Phase transitions and finite-size scaling Critical slowing down and cluster methods. Theory of phase transitions/ RNG Finite-size scaling Detailed treatment: Lectures on Phase Transitions and the Renormalization
More informationGPU-based computation of the Monte Carlo simulation of classical spin systems
Perspectives of GPU Computing in Physics and Astrophysics, Sapienza University of Rome, Rome, Italy, September 15-17, 2014 GPU-based computation of the Monte Carlo simulation of classical spin systems
More informationUniversal critical behavior of the two-dimensional Ising spin glass
PHYSICAL REVIEW B 94, 024402 (2016) Universal critical behavior of the two-dimensional Ising spin glass L. A. Fernandez, 1,2 E. Marinari, 3,4 V. Martin-Mayor, 1,2 G. Parisi, 3,4 and J. J. Ruiz-Lorenzo
More informationPhase Transitions in Disordered Systems: The Example of the 4D Random Field Ising Model
Phase Transitions in Disordered Systems: The Example of the 4D Random Field Ising Model Nikos Fytas Applied Mathematics Research Centre, Coventry University, United Kingdom Work in collaboration with V.
More informationCritical Behaviour of the 3D XY -Model: A Monte Carlo Study
KL-TH-93/10 CERN-TH.6885/93 Critical Behaviour of the 3D XY -Model: A Monte Carlo Study arxiv:cond-mat/9305020v1 18 May 1993 Aloysius P. Gottlob Universität Kaiserslautern, D-6750 Kaiserslautern, Germany
More informationScaling Theory. Roger Herrigel Advisor: Helmut Katzgraber
Scaling Theory Roger Herrigel Advisor: Helmut Katzgraber 7.4.2007 Outline The scaling hypothesis Critical exponents The scaling hypothesis Derivation of the scaling relations Heuristic explanation Kadanoff
More informationNumerical Analysis of 2-D Ising Model. Ishita Agarwal Masters in Physics (University of Bonn) 17 th March 2011
Numerical Analysis of 2-D Ising Model By Ishita Agarwal Masters in Physics (University of Bonn) 17 th March 2011 Contents Abstract Acknowledgment Introduction Computational techniques Numerical Analysis
More informationarxiv:cond-mat/ v2 [cond-mat.stat-mech] 7 Jun 2004
Critical behavior of O(2) O(N) symmetric models arxiv:cond-mat/0405667v2 [cond-mat.stat-mech] 7 Jun 2004 Pasquale Calabrese, 1 Pietro Parruccini, 2 Andrea Pelissetto, 3 and Ettore Vicari 4 1 R. Peierls
More informationParallel tempering and 3D spin glass models
Journal of Physics: Conference Series OPEN ACCESS Parallel tempering and 3D spin glass models To cite this article: T Papakonstantinou and A Malakis 2014 J. Phys.: Conf. Ser. 487 012010 View the article
More information4. Cluster update algorithms
4. Cluster update algorithms Cluster update algorithms are the most succesful global update methods in use. These methods update the variables globally, in one step, whereas the standard local methods
More informationMonte Caro simulations
Monte Caro simulations Monte Carlo methods - based on random numbers Stanislav Ulam s terminology - his uncle frequented the Casino in Monte Carlo Random (pseudo random) number generator on the computer
More informationMonte Carlo study of the Baxter-Wu model
Monte Carlo study of the Baxter-Wu model Nir Schreiber and Dr. Joan Adler Monte Carlo study of the Baxter-Wu model p.1/40 Outline Theory of phase transitions, Monte Carlo simulations and finite size scaling
More informationIs the Sherrington-Kirkpatrick Model relevant for real spin glasses?
Is the Sherrington-Kirkpatrick Model relevant for real spin glasses? A. P. Young Department of Physics, University of California, Santa Cruz, California 95064 E-mail: peter@physics.ucsc.edu Abstract. I
More informationCritical Dynamics of Two-Replica Cluster Algorithms
University of Massachusetts Amherst From the SelectedWorks of Jonathan Machta 2001 Critical Dynamics of Two-Replica Cluster Algorithms X. N. Li Jonathan Machta, University of Massachusetts Amherst Available
More informationarxiv:hep-lat/ v1 20 Sep 2002
Monte Carlo studies of three-dimensional O(1) and O(4) φ 4 theory related to BEC phase transition temperatures Xuepeng Sun Department of Physics, University of Virginia, P.O. Box 4714, Charlottesville,
More informationarxiv:cond-mat/ v2 [cond-mat.dis-nn] 11 Nov 2009
arxiv:cond-mat/0611568v2 [cond-mat.dis-nn] 11 Nov 2009 On the universality class of the 3d Ising model with long-range-correlated disorder D. Ivaneyko a,, B. Berche b, Yu. Holovatch c,d, J. Ilnytskyi c,e
More informationarxiv: v1 [cond-mat.stat-mech] 27 Oct 2014
Thermodynamic Casimir Effect in Films: the Exchange Cluster Algorithm arxiv:1410.7161v1 [cond-mat.stat-mech] 27 Oct 2014 Martin Hasenbusch Institut für Physik, Humboldt-Universität zu Berlin, Newtonstr.
More informationPhase Transitions of Random Binary Magnetic Square Lattice Ising Systems
I. Q. Sikakana Department of Physics and Non-Destructive Testing, Vaal University of Technology, Vanderbijlpark, 1900, South Africa e-mail: ike@vut.ac.za Abstract Binary magnetic square lattice Ising system
More informationMonte Carlo Simulation of the 2D Ising model
Monte Carlo Simulation of the 2D Ising model Emanuel Schmidt, F44 April 6, 2 Introduction Monte Carlo methods are a powerful tool to solve problems numerically which are dicult to be handled analytically.
More informationLogarithmic corrections to gap scaling in random-bond Ising strips
J. Phys. A: Math. Gen. 30 (1997) L443 L447. Printed in the UK PII: S0305-4470(97)83212-X LETTER TO THE EDITOR Logarithmic corrections to gap scaling in random-bond Ising strips SLAdeQueiroz Instituto de
More informationA Monte Carlo Implementation of the Ising Model in Python
A Monte Carlo Implementation of the Ising Model in Python Alexey Khorev alexey.s.khorev@gmail.com 2017.08.29 Contents 1 Theory 1 1.1 Introduction...................................... 1 1.2 Model.........................................
More informationPopulation annealing study of the frustrated Ising antiferromagnet on the stacked triangular lattice
Population annealing study of the frustrated Ising antiferromagnet on the stacked triangular lattice Michal Borovský Department of Theoretical Physics and Astrophysics, University of P. J. Šafárik in Košice,
More informationarxiv:cond-mat/ v2 [cond-mat.stat-mech] 3 Dec 2004
Condensed Matter Physics, 200?, Vol.?, No?, pp. 1?? arxiv:cond-mat/0411255v2 [cond-mat.stat-mech] 3 Dec 2004 Random Ising model in three dimensions: theory, experiment and simulation a difficult coexistence
More informationarxiv:hep-lat/ v2 8 Jan 2003
Dynamical generation of a gauge symmetry in the Double-Exchange model arxiv:hep-lat/0301004v2 8 Jan 2003 J.M. Carmona a, A. Cruz a,e, L. A. Fernández b,e, S. Jiménez a,e, V. Martín-Mayor b,e, A. Muñoz-Sudupe
More informationNon-standard finite-size scaling at first-order phase transitions
Non-standard finite-size scaling at first-order phase transitions Marco Mueller, Wolfhard Janke, Des Johnston Coventry MECO39, April 2014 Mueller, Janke, Johnston Non-Standard First Order 1/24 Plan of
More informationPhase Transitions in Spin Glasses
p.1 Phase Transitions in Spin Glasses Peter Young http://physics.ucsc.edu/ peter/talks/bifi2008.pdf e-mail:peter@physics.ucsc.edu Work supported by the and the Hierarchical Systems Research Foundation.
More information0. Construction of d-dimensional Isotropic and Anisotropic Hierarchical Lattices 1. Frustrated Systems and Chaotic Renormalization- Group
Hierarchical Lattices: Renormalization-Group Solutions of Plain, Anisotropic,Chaotic, Heterogeneous, and Clustered Systems Collaborators: D. Andelman, A. Erbaş, A. Falicov, K. Hui, M. Hinczewski, A. Kabakçıoğlu,
More informationEvaporation/Condensation of Ising Droplets
, Elmar Bittner and Wolfhard Janke Institut für Theoretische Physik, Universität Leipzig, Augustusplatz 10/11, D-04109 Leipzig, Germany E-mail: andreas.nussbaumer@itp.uni-leipzig.de Recently Biskup et
More informationMacroscopic Degeneracy and FSS at 1st Order Phase Transitions
Macroscopic Degeneracy and FSS at 1st Order Phase Transitions Marco Mueller (hero), Wolfhard Janke (good guy), Des Johnston (villain) Krakow, Oct 2015 Mueller, Janke, Johnston Degeneracy/FSS 1/22 Plan
More informationPotts And XY, Together At Last
Potts And XY, Together At Last Daniel Kolodrubetz Massachusetts Institute of Technology, Center for Theoretical Physics (Dated: May 16, 212) We investigate the behavior of an XY model coupled multiplicatively
More informationMetropolis Monte Carlo simulation of the Ising Model
Metropolis Monte Carlo simulation of the Ising Model Krishna Shrinivas (CH10B026) Swaroop Ramaswamy (CH10B068) May 10, 2013 Modelling and Simulation of Particulate Processes (CH5012) Introduction The Ising
More informationSimulation of the two-dimensional square-lattice Lenz-Ising model in Python
Senior Thesis Simulation of the two-dimensional square-lattice Lenz-Ising model in Python Author: Richard Munroe Advisor: Dr. Edward Brash 2012-10-17 Abstract A program to simulate the the two-dimensional
More informationLecture 8: Computer Simulations of Generalized Ensembles
Lecture 8: Computer Simulations of Generalized Ensembles Bernd A. Berg Florida State University November 6, 2008 Bernd A. Berg (FSU) Generalized Ensembles November 6, 2008 1 / 33 Overview 1. Reweighting
More informationarxiv: v1 [cond-mat.dis-nn] 23 Apr 2008
lack of monotonicity in spin glass correlation functions arxiv:0804.3691v1 [cond-mat.dis-nn] 23 Apr 2008 Pierluigi Contucci, Francesco Unguendoli, Cecilia Vernia, Dipartimento di Matematica, Università
More informationPhase transitions in the Potts spin-glass model
PHYSICAL REVIEW E VOLUME 58, NUMBER 3 SEPTEMBER 1998 Phase transitions in the Potts spin-glass model Giancarlo Franzese 1 and Antonio Coniglio 1,2 1 Dipartimento di Scienze Fisiche, Università di Napoli,
More informationFinite size effects on measures of critical exponents in d = 3 0 ( IV) models
10 October 1996 PHYSICS LETTERS B Physics Letters B 387 (1996) 125-131 Finite size effects on measures of critical exponents in d = 3 0 ( IV) models H.G. Ballesteros, L. A. Fern&dez2, V. Martin-Mayor 3,
More informationPhase Transition in Vector Spin Glasses. Abstract
Phase Transition in Vector Spin Glasses A. P. Young Department of Physics, University of California, Santa Cruz, California 95064 (Dated: June 3, 2004) Abstract We first give an experimental and theoretical
More informationarxiv:hep-lat/ v1 24 Mar 2000
CERN-TH/2000-080 NORDITA-2000/29HE hep-lat/0003020 O(2) SYMMETRY BREAKING VS. VORTEX LOOP PERCOLATION arxiv:hep-lat/0003020v1 24 Mar 2000 K. Kajantie a,1, M. Laine b,a,2, T. Neuhaus c,d,3, A. Rajantie
More informationMonte Carlo tests of theoretical predictions for critical phenomena: still a problem?
Computer Physics Communications 127 (2) 126 13 www.elsevier.nl/locate/cpc Monte Carlo tests of theoretical predictions for critical phenomena: still a problem? K. Binder, E. Luijten Johannes-Gutenberg-Universität,
More informationPhysics 212: Statistical mechanics II Lecture XI
Physics 212: Statistical mechanics II Lecture XI The main result of the last lecture was a calculation of the averaged magnetization in mean-field theory in Fourier space when the spin at the origin is
More informationExact solutions to plaquette Ising models with free and periodic boundaries
Exact solutions to plaquette Ising models with free and periodic boundaries Marco Mueller 1 W. Janke 1 and D. A. Johnston 2 1 Institut für theoretische Physik, Universität Leipzig, Germany 2 Department
More informationThe Phase Transition of the 2D-Ising Model
The Phase Transition of the 2D-Ising Model Lilian Witthauer and Manuel Dieterle Summer Term 2007 Contents 1 2D-Ising Model 2 1.1 Calculation of the Physical Quantities............... 2 2 Location of the
More informationDirectional Ordering in the Classical Compass Model in Two and Three Dimensions
Institut für Theoretische Physik Fakultät für Physik und Geowissenschaften Universität Leipzig Diplomarbeit Directional Ordering in the Classical Compass Model in Two and Three Dimensions vorgelegt von
More informationNon-trivial θ-vacuum Effects in the 2-d O(3) Model
Non-trivial θ-vacuum Effects in the 2-d O(3) Model Uwe-Jens Wiese Albert Einstein Center for Fundamental Physics Institute for Theoretical Physics, Bern University CERN, August 2, 2012 Collaborators: Wolfgang
More informationA New Method to Determine First-Order Transition Points from Finite-Size Data
A New Method to Determine First-Order Transition Points from Finite-Size Data Christian Borgs and Wolfhard Janke Institut für Theoretische Physik Freie Universität Berlin Arnimallee 14, 1000 Berlin 33,
More informationQuantum phase transitions of insulators, superconductors and metals in two dimensions
Quantum phase transitions of insulators, superconductors and metals in two dimensions Talk online: sachdev.physics.harvard.edu HARVARD Outline 1. Phenomenology of the cuprate superconductors (and other
More informationMicroscopic Deterministic Dynamics and Persistence Exponent arxiv:cond-mat/ v1 [cond-mat.stat-mech] 22 Sep 1999
Microscopic Deterministic Dynamics and Persistence Exponent arxiv:cond-mat/9909323v1 [cond-mat.stat-mech] 22 Sep 1999 B. Zheng FB Physik, Universität Halle, 06099 Halle, Germany Abstract Numerically we
More informationQuantum Monte Carlo Simulations in the Valence Bond Basis. Anders Sandvik, Boston University
Quantum Monte Carlo Simulations in the Valence Bond Basis Anders Sandvik, Boston University Outline The valence bond basis for S=1/2 spins Projector QMC in the valence bond basis Heisenberg model with
More informationarxiv:cond-mat/ v1 [cond-mat.stat-mech] 27 Aug 2002
arxiv:cond-mat/0208521v1 [cond-mat.stat-mech] 27 Aug 2002 EUROPHYSICS LETTERS Europhys. Lett., xx (x), pp. 1-7 (2002) today Correlations in the low-temperature phase of the twodimensional XY model B. Berche
More informationIntroduction to the Renormalization Group
Introduction to the Renormalization Group Gregory Petropoulos University of Colorado Boulder March 4, 2015 1 / 17 Summary Flavor of Statistical Physics Universality / Critical Exponents Ising Model Renormalization
More informationProgress toward a Monte Carlo Simulation of the Ice VI-VII Phase Transition
Progress toward a Monte Carlo Simulation of the Ice VI-VII Phase Transition Christina Gower 2010 NSF/REU PROJECT Physics Department University of Notre Dame Advisor: Dr. Kathie E. Newman August 6, 2010
More informationScale-Free Enumeration of Self-Avoiding Walks on Critical Percolation Clusters
Scale-Free Enumeration of Self-Avoiding Walks on Critical Percolation Clusters Niklas Fricke and Wolfhard Janke Institut für Theoretische Physik, Universität Leipzig November 29, 2013 Self-avoiding walk
More informationClusters and Percolation
Chapter 6 Clusters and Percolation c 2012 by W. Klein, Harvey Gould, and Jan Tobochnik 5 November 2012 6.1 Introduction In this chapter we continue our investigation of nucleation near the spinodal. We
More informationthe renormalization group (RG) idea
the renormalization group (RG) idea Block Spin Partition function Z =Tr s e H. block spin transformation (majority rule) T (s, if s i ; s,...,s 9 )= s i > 0; 0, otherwise. b Block Spin (block-)transformed
More informationarxiv: v1 [cond-mat.dis-nn] 12 Nov 2014
Representation for the Pyrochlore Lattice arxiv:1411.3050v1 [cond-mat.dis-nn] 12 Nov 2014 André Luis Passos a, Douglas F. de Albuquerque b, João Batista Santos Filho c Abstract a DFI, CCET, Universidade
More informationClassical Monte Carlo Simulations
Classical Monte Carlo Simulations Hyejin Ju April 17, 2012 1 Introduction Why do we need numerics? One of the main goals of condensed matter is to compute expectation values O = 1 Z Tr{O e βĥ} (1) and
More informationConnected spatial correlation functions and the order parameter of the 3D Ising spin glass
Connected spatial correlation functions and the order parameter of the 3D Ising spin glass David Yllanes for the Janus Collaboration 1 Dep. Física Teórica, Universidad Complutense de Madrid http://teorica.fis.ucm.es/grupos/grupo-tec.html
More informationPhase Transition in Vector Spin Glasses. Abstract
Phase Transition in Vector Spin Glasses A. P. Young Department of Physics, University of California, Santa Cruz, California 95064 (Dated: June 2, 2004) Abstract We first give an experimental and theoretical
More informationin three-dimensional three-state random bond Potts model (α >0f for a disordered d dsystem in 3D)
Positive specific heat critical exponent in three-dimensional three-state random bond Potts model (α >0f for a disordered d dsystem in 3D) ZHONG Fan School of Physics and Engineering Sun Yat-sen University
More informationThe Ising model Summary of L12
The Ising model Summary of L2 Aim: Study connections between macroscopic phenomena and the underlying microscopic world for a ferromagnet. How: Study the simplest possible model of a ferromagnet containing
More informationQuantum Monte Carlo Simulations in the Valence Bond Basis
NUMERICAL APPROACHES TO QUANTUM MANY-BODY SYSTEMS, IPAM, January 29, 2009 Quantum Monte Carlo Simulations in the Valence Bond Basis Anders W. Sandvik, Boston University Collaborators Kevin Beach (U. of
More informationarxiv:cond-mat/ v2 [cond-mat.dis-nn] 26 Sep 2006
Critical behavior of the three- and ten-state short-range Potts glass: A Monte Carlo study arxiv:cond-mat/0605010v2 [cond-mat.dis-nn] 26 Sep 2006 L. W. Lee, 1 H. G. Katzgraber, 2 and A. P. Young 1, 1 Department
More information8.334: Statistical Mechanics II Problem Set # 4 Due: 4/9/14 Transfer Matrices & Position space renormalization
8.334: Statistical Mechanics II Problem Set # 4 Due: 4/9/14 Transfer Matrices & Position space renormalization This problem set is partly intended to introduce the transfer matrix method, which is used
More informationarxiv:hep-lat/ v1 9 Mar 1994
Correlation Function in Ising Models arxiv:hep-lat/9403009v1 9 Mar 1994 C. Ruge a, P. Zhu b and F. Wagner a a) Institut für Theoretische Physik und Sternwarte Univ. Kiel, D-24098 Kiel, Germany E Mail:
More informationUniversal effective coupling constant ratios of 3D scalar φ 4 field theory and pseudo-ɛ expansion
Universal effective coupling constant ratios of 3D scalar φ 4 field theory and pseudo-ɛ expansion A. I. Sokolov 1,, M. A. Nikitina 1,2, and A. Kudlis 1,2, 1 Department of Quantum Mechanics, Saint Petersburg
More informationGuiding Monte Carlo Simulations with Machine Learning
Guiding Monte Carlo Simulations with Machine Learning Yang Qi Department of Physics, Massachusetts Institute of Technology Joining Fudan University in 2017 KITS, June 29 2017. 1/ 33 References Works led
More informationPHYSICAL REVIEW LETTERS
PHYSICAL REVIEW LETTERS VOLUME 76 4 MARCH 1996 NUMBER 10 Finite-Size Scaling and Universality above the Upper Critical Dimensionality Erik Luijten* and Henk W. J. Blöte Faculty of Applied Physics, Delft
More informationLearning About Spin Glasses Enzo Marinari (Cagliari, Italy) I thank the organizers... I am thrilled since... (Realistic) Spin Glasses: a debated, inte
Learning About Spin Glasses Enzo Marinari (Cagliari, Italy) I thank the organizers... I am thrilled since... (Realistic) Spin Glasses: a debated, interesting issue. Mainly work with: Giorgio Parisi, Federico
More informationLOCAL MOMENTS NEAR THE METAL-INSULATOR TRANSITION
LOCAL MOMENTS NEAR THE METAL-INSULATOR TRANSITION Subir Sachdev Center for Theoretical Physics, P.O. Box 6666 Yale University, New Haven, CT 06511 This paper reviews recent progress in understanding the
More informationarxiv:cond-mat/ v1 [cond-mat.stat-mech] 6 Jun 1997
arxiv:cond-mat/9706065v1 [cond-mat.stat-mech] 6 Jun 1997 LETTER TO THE EDITOR Logarithmic corrections to gap scaling in random-bond Ising strips S L A de Queiroz Instituto de Física, UFF, Avenida Litorânea
More informationMonte Carlo study of O 3 antiferromagnetic models in three dimensions
PHYSICAL REVIEW B VOLUME 53, NUMBER 5 1 FEBRUARY 1996-I Monte Carlo study of O 3 antiferromagnetic models in three dimensions J. L. Alonso and A. Tarancón Departamento de Física Teórica, Facultad de Ciencias,
More informationICCP Project 2 - Advanced Monte Carlo Methods Choose one of the three options below
ICCP Project 2 - Advanced Monte Carlo Methods Choose one of the three options below Introduction In statistical physics Monte Carlo methods are considered to have started in the Manhattan project (1940
More informationQuantum Annealing in spin glasses and quantum computing Anders W Sandvik, Boston University
PY502, Computational Physics, December 12, 2017 Quantum Annealing in spin glasses and quantum computing Anders W Sandvik, Boston University Advancing Research in Basic Science and Mathematics Example:
More informationMonte Carlo Simulation of Spins
Monte Carlo Simulation of Spins Aiichiro Nakano Collaboratory for Advanced Computing & Simulations Department of Computer Science Department of Physics & Astronomy Department of Chemical Engineering &
More information8 Error analysis: jackknife & bootstrap
8 Error analysis: jackknife & bootstrap As discussed before, it is no problem to calculate the expectation values and statistical error estimates of normal observables from Monte Carlo. However, often
More informationConstrained tricritical Blume-Capel model in three dimensions
PHYSICAL REVIEW E 70, 046111 (2004) Constrained tricritical Blume-Capel model in three dimensions Youjin Deng 1 and Henk W. J. Blöte 1,2 1 Laboratory for Material Science, Delft University of Technology,
More information3. General properties of phase transitions and the Landau theory
3. General properties of phase transitions and the Landau theory In this Section we review the general properties and the terminology used to characterise phase transitions, which you will have already
More informationComplex Systems Methods 9. Critical Phenomena: The Renormalization Group
Complex Systems Methods 9. Critical Phenomena: The Renormalization Group Eckehard Olbrich e.olbrich@gmx.de http://personal-homepages.mis.mpg.de/olbrich/complex systems.html Potsdam WS 2007/08 Olbrich (Leipzig)
More informationPhase transitions and critical phenomena
Phase transitions and critical phenomena Classification of phase transitions. Discontinous (st order) transitions Summary week -5 st derivatives of thermodynamic potentials jump discontinously, e.g. (
More informationRenormalization Group: non perturbative aspects and applications in statistical and solid state physics.
Renormalization Group: non perturbative aspects and applications in statistical and solid state physics. Bertrand Delamotte Saclay, march 3, 2009 Introduction Field theory: - infinitely many degrees of
More informationarxiv:cond-mat/ v1 [cond-mat.stat-mech] 17 Sep 1999
Shape Effects of Finite-Size Scalin Functions for Anisotropic Three-Dimensional Isin Models Kazuhisa Kaneda and Yutaka Okabe Department of Physics, Tokyo Metropolitan University, Hachioji, Tokyo 92-397,
More informationMassimo D Elia Dipartimento di Fisica and INFN Genova, Via Dodecaneso 33, I Genova, ITALY
A test of first order scaling of the N f =2 QCD phase transition Guido Cossu SNS and INFN Pisa, Piazza dei Cavalieri 7, I-56127 Pisa, ITALY g.cossu@sns.it Massimo D Elia Dipartimento di Fisica and INFN
More informationCritical Behaviors and Finite-Size Scaling of Principal Fluctuation Modes in Complex Systems
Commun. Theor. Phys. 66 (2016) 355 362 Vol. 66, No. 3, September 1, 2016 Critical Behaviors and Finite-Size Scaling of Principal Fluctuation Modes in Complex Systems Xiao-Teng Li ( 李晓腾 ) and Xiao-Song
More informationValence Bonds in Random Quantum Magnets
Valence Bonds in Random Quantum Magnets theory and application to YbMgGaO 4 Yukawa Institute, Kyoto, November 2017 Itamar Kimchi I.K., Adam Nahum, T. Senthil, arxiv:1710.06860 Valence Bonds in Random Quantum
More informationIsing Model. Ising Lattice. E. J. Maginn, J. K. Shah
Ising Lattice E. J. Maginn, J. K. Shah Department of Chemical and Biomolecular Engineering University of Notre Dame Notre Dame, IN 46556 USA Monte Carlo Workshop, Brazil Ising Lattice Model Consider a
More informationMonte Carlo Renormalization of 2d Simplicial Quantum Gravity Coupled to Gaussian Matter
Syracuse University SURFACE Physics College of Arts and Sciences 9-17-1998 Monte Carlo Renormalization of 2d Simplicial Quantum Gravity Coupled to Gaussian Matter Simon Catterall Syracuse University Eric
More informationAgeing properties of three-dimensional pure and site-diluted Ising ferromagnets
Journal of Physics: Conference Series OPEN ACCESS Ageing properties of three-dimensional pure and site-diluted Ising ferromagnets To cite this article: Vladimir V Prudnikov et al 2014 J. Phys.: Conf. Ser.
More information